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arXiv · 1806.07101

Slopes of 3-dimensional Subshifts of Finite Type

Etienne Moutot·Pascal Vanier
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Abstract

In this paper we study the directions of periodicity of three-dimensional subshifts of finite type (SFTs) and in particular their slopes. A configuration of a subshift has a slope of periodicity if it is periodic in exactly one direction, the slope being the angle of the periodicity vectors. In this paper, we prove that any $\Sigma^0_2$ set may be realized as a a set of slopes of an SFT.

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Etienne Moutot, Pascal Vanier. 2018-06-19. Slopes of 3-dimensional Subshifts of Finite Type. https://doi.org/10.1007/978-3-319-90530-3_22

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